On your work surface, pound the chicken breasts to flatten them. You can use plastic wrap or waxed paper to wrap around the chicken and beat with the bottom of a skillet.
Sprinkle salt and pepper over both sides of the flattened chicken.
In a large skillet, add 1 tablespoon each of butter and olive oil. When the butter has melted, add the chicken breasts. Cook over medium heat 3-4 minutes per side. Remove the chicken with a slotted spoon and set aside.
Add the dijon mustard, green onions, parseley, and lemon/lime juice to the skillet and whisk for about 30 seconds. Whisk in the chicken stock and stir gently until the sauce becomes creamy and begins to thicken slightly. Add the remaining butter and olive oil.
When the sauce has become smooth, return the chicken to the sauce in the pan and simmer for a minute to reheat the chicken.
Serve with rice, wild rice, or buttered and parselied pasta. A salad goes well with this.
You can substitute a cup of wine (even a not-too-dry red wine) for the chicken stock.